Bach never had a back porch, but he did enjoy writing for instruments with irregularities and limitations. He could actually play the lute, which however went out of vogue during his lifetime, so his compositions for it were but few.

Yes, he may have enjoyed the challenge to compose for banjo, but only few banjo players would enjoy practising his music. Those who double as guitarists may well try his lute music (which takes some slight tweaking).

The idea of "mathematical music" has fascinated many people for millennia, but I think it is too vague a concept to be of any use. To be sure, writing fugues atc. requires some elementary mathematics, but Bach and other great composers have a lot more to offer.